Problem: Solve for $x$ and $y$ using elimination. ${2x+5y = 41}$ ${-2x+6y = 14}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $11y = 55$ $\dfrac{11y}{{11}} = \dfrac{55}{{11}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {2x+5y = 41}\thinspace$ to find $x$ ${2x + 5}{(5)}{= 41}$ $2x+25 = 41$ $2x+25{-25} = 41{-25}$ $2x = 16$ $\dfrac{2x}{{2}} = \dfrac{16}{{2}}$ ${x = 8}$ You can also plug ${y = 5}$ into $\thinspace {-2x+6y = 14}\thinspace$ and get the same answer for $x$ : ${-2x + 6}{(5)}{= 14}$ ${x = 8}$